Topic: The Casimir Effect: new manifestations and simplified analysis February 2

Presenter: Oded Kenneth, Tel Aviv University

Topic: Physics and mathematics of oscillatory integrals February 4

Presenter: Slava Rychkov, Princeton University

Abstract: We will have fun with a number of things related to short-wave asymptotics of oscillatory integrals. Probably the easiest physical interpretation of the theory is the intensity of light near caustics. The method of calculating the asymptotics is based on resolving the singularities of the phase function by pulling it back to a toric variety. The construction is governed by the Newton polyhedron of the phase function.

Topic: Topology and Sobolev spaces February 4

Presenter: Yanyan Li, Rutgers University

Topic: Geometric analysis of Chow-Mumford stability February 4

Presenter: Sean Paul, Princeton University

Topic: Vorticity in the Ginzburg-Landau model of superconductivity February 7

Presenter: Sylvia Sefraty, L'Ecole Normale Superieure de Cachan

Abstract: The Ginzburg-Landau functional $$J(u,A)=\frac{1}{2}\int_{\Omega} |\nabla_A u|^2 + |h-h_{ex}|^2 + \frac{1}{2\epsilon^2} (1-|u|^2)^2,$$ is the energy of a superconductor submitted to a magnetic field $h_{ex}$. The main feature is the apparition of vortices for certain values of the applied field. After the work of Bethuel- Brezis- Helein on a simplified energy (without magnetic field), we (partly joint work with E. Sandier) have studied this full functional in the asymptotics of small $\,\epsilon$, and developed a similar analysis for it. We have particularly focused on describing the energy-minimizing configurations, their vortices, and determining a mean-vorticity measure.

Topic: Micromagnetic Modeling of Magnetic Thin Films and Its Applications February 7

Presenter: Jimmy Zhu, Department of Electrical and Computer

Engineering, Carnegie Mellon University

Abstract: Micromagnetic modeling has become a powerful tool for understanding complicated microscopic dynamicmagnetization processes in thin magnetic films. It also has become a very useful tool for aiding device designs over the recent years. In this talk, micromagnetic modeling work on thin magnetic films will be reviewed. Computer simulations on magnetization reversal processes on films patterned into different geometry and comparison with the corresponding experimental observations will be discussed. The talk will also cover applications utilizing micromagnetic modeling to aid the designs of magnetic random access memory (MRAM) and the engineering of material microstructures for thin film recording media in disk drive applications.

Topic: On the supersingular locus of Hilbert modular varieties February 8

Presenter: C-F Yu, Columbia University

Topic: Turning questions into games February 9

Presenter: Joe Killian, NEC

Topic: Lagrangian torus fibration of Calabi-Yau hypersurfaces February 10

and mirror symmetry

Presenter: Wei-Dong Ruan, Columbia University

Topic: Unextendible Product Bases February 11

Presenter: Noga Alon, Tel Aviv University

Abstract: An unextendible product basis is a maximal (with respect to containment) set of pairwise orthogonal nonzero vectors in the tensor product of finite dimensional vector spaces over the complex field, whose cardinality is strictly smaller than the dimension of the corresponding tensor product. The study of such bases is motivated by problems in quantum information theory.

If the dimensions of the vector spaces are a_1, a_2,.., a_m, then the cardinality of any unextendible product basis in their product is at least 1+(a_1-1)+(a_2-1)+...+(a_m-1). We determine all cases of equality by combining results about orthogonal representations of graphs with techniques from additive number theory.

Joint work with L. Lovasz.

Topic: A new variational characterization of thre-dimensional space forms February 11

Presenter: Matthew Gursky, Indiana University

Topic: Gluing constructions for minimal surfaces in R^3 and S^3 February 11

Presenter: Seong-Deog Yang, Indiana University

Topic: L^2 harmonic forms on some Kaehler manifolds February 14

Presenter: Jeff McNeal, Ohio State University

Topic: On some problems from ergodic theory and the theory of Dynamical Systems

Presenter: Bendjamen Weiss, Hebrew University of Jerusalem

Topic: On a very nice family of Hecke characters and elliptic curves February 15

Presenter: T.H. Yang, SUNY, Stony Brook

Topic: Equations of motion in gravity theories February 15

Presenter: S. Kaniel, Hebrew University Jerusalem

Topic: Adiabatic Pistons as a Dynamical System February 17

Presenter: Ya G. Sinai, Princeton University

Topic: Global secular dynamics in the planar three-body problem March 23

Presenter: Jacques Fejoz, Northwestern University